Problem: Jessica is 2 times as old as Tiffany. 28 years ago, Jessica was 6 times as old as Tiffany. How old is Jessica now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Tiffany. Let Jessica's current age be $j$ and Tiffany's current age be $t$ The information in the first sentence can be expressed in the following equation: $j = 2t$ 28 years ago, Jessica was $j - 28$ years old, and Tiffany was $t - 28$ years old. The information in the second sentence can be expressed in the following equation: $j - 28 = 6(t - 28)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $t$ and substitute it into our second equation. Solving our first equation for $t$ , we get: $t = j / 2$ . Substituting this into our second equation, we get: $j - 28 = 6($ $(j / 2)$ $- 28)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 28 = 3 j - 168$ Solving for $j$ , we get: $2 j = 140$ $j = \dfrac{1}{2} \cdot 140 = 70$.